The complex coordinate rotation method and exterior scaling: A simple example

This is the authors' abstract. We don't add key points for this paper.

The so-called complex coordinate rotation technique is applied to two simple one-dimensional piecewise-defined model potentials. The invariance of the bound and resonance energy levels of these potentials under coordinate rotation is analyzed. It is shown that a proper treatment of the coordinate rotation gives a natural and easily understood introduction of the so-called exterior scaling. Implications for application of the coordinate rotation method to physically reasonable electron-atom or electron-molecule potentials are also discussed. Finally, the relative merits of the rotation procedure and the direct Siegert search method proposed by Miller et al. are evaluated.